International Journal of Electrical and Electronics Engineering Research (IJEEER) ISSN 2250-155X Vol. 2 Issue 4 Dec - 2012 65-72 © TJPRC Pvt. Ltd.,
REVIEW OF MITIGATION OF HARMONICS IN MULTILEVEL INVERTERS USING PSO ANKITA PAPRIWAL1 & AMITA MAHOR2 1
P.G. Scholer, NIIST, Bhopal (M.P.), India
2
H.O.D, Electrical & Electronics Department, NIIST, Bhopal(M.P.), India
ABSTRACT Multilevel inverter technology has emerged recently as a very important alternative in the area of high-power medium-voltage energy control. Using multilevel inverters application in fuel cell, solar cell & wind turbines is increasing now a day’s rapidly. Therefore, Harmonic reduction techniques in multilevel inverters are considered very important task. For eliminating the harmonics PSO algorithm is used. Particle swarm optimization (PSO) is an effective & reliable evolutionary based approach .Due to its higher quality solution including mathematical simplicity, fast convergence & robustness it has become popular for many optimization problems. This paper presents a review application of PSO for harmonic reduction in Multilevel inverters.
KEY WORDS: Harmonic suppression, Multilevel Inverter, PSO,Total Harmonic Distortion INTRODUCTION Multilevel inverters have drawn tremendous interest in the field of high-voltage high-power applications such as laminators, mills, conveyors, compressors, large induction motor drives, UPS systems, and static var compensation level by connecting different dc sources of lower. Some of the fundamental multilevel topologies include the diode-clamped, flying capacitor, and cascaded H-bridge structures. The most familiar power circuit topology for multilevel converters is based on the cascade connection of an s number of single-phase full-bridge inverters to generate a (2s + 1) number of levels. The key issue in designing an effective multilevel inverter is to ensure that the total harmonic distortion (THD) of the output voltage waveform is within acceptable limits. Basically, there are four types of control methods for multilevel converters. They are the fundamental frequency switching method, space vector control method, traditional PWM control method and space vector PWM method .The fundamental frequency switching and space vector control methods have the benefit of low switching frequency, although they have high low-order harmonics at low modulation indices as compared to the other two control methods. Generally, the traditional PWM method is widely used for harmonic elimination. But PWM techniques are not able to eliminate low-order harmonics completely. Another approach is to choose switching angles so that specific lower order dominant harmonics are suppressed. The elimination of specific low-order harmonics from a given voltage /current waveform generated by a voltage/current source inverter using what is widely known as optimal , “Programmed” or selective harmonic elimination PWM (SHE-PWM) techniques has been used for various converter topologies, systems, and applications. The output voltage waveform analysis using Fourier theory produces a set of non-linear transcendental equations. The solution of these equations, if exists, gives the switching angles required for certain fundamental component and selected harmonic profile. Iterative procedures such as Newton-Raphson method has been used to solve these sets of equations. This method is derivative-dependent and may end in local optima, and a judicious choice of the initial values alone guarantees conversion. Another approach based on converting the transcendental equation into polynomial equations is presented in,
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where resultant theory is applied to determine the switching angles to eliminate specific harmonics. This approach, however, appears to be unattractive because as the number of inverter level increases, so does the degree of the polynomials of the mathematical model. This is likely to lead to numerical difficulty and substantial computational burden as well. Genetic algorithms (GA) have been used to obtain optimal solutions for inverter circuits supplied from constant dc sources. Despite their effectiveness in selective harmonic elimination, they are complicated and their parameters such as crossover and mutation probability, population size and number of generations are usually selected as common values given in literature or by means of a trial and error process to achieve the best solution set. Heuristic algorithms such as Particle Swarm Optimization (PSO) have the ability to combat the above drawbacks. Particle Swarm Optimization (PSO) is a relatively recent heuristic search method whose mechanics are inspired by the swarming or collaborative behaviour of biological populationsAs an optimization technique, PSO is much less dependent on the start values of the variables in the optimization problem when compared with the widely used Newton-Raphson. In addition, PSO doesn’t relay on the guidance of the gradient information, such as the Jacobian matrix, hence it is more capable of determining the global optimum solution. PSO deal with all problems that usually considered very hard such as integer variables, non-convex functions, no differentiable functions, domains not connected, badly behaved functions, multiple local optima, and multiple objectives. For these reasons, PSO has been adopted in this study. The main objective is to propose a method for optimization of specific harmonics and improving the characteristics of switching in multilevel inverters. The switching angle of each levels and the output voltage of them is determined and is used for optimization. Then the effect of changing in the output voltage of each inverter on reduction of one or more specific harmonic is analyzed. For a low number of switching angles, the proposed PSO approach reduces the computational burden to find the optimal solution compared with iterative methods and the resultant theory approach. The proposed method solves the asymmetry of the transcendental equation set, which has to be solved in cascade multilevel inverters.
CASCADED H-BRIDGE MULTILEVEL INVERTER A single-phase structure of an m-level cascaded inverter is illustrated in Fig. Each separate dc source (SDCS) is connected to a single-phase full-bridge, or H-bridge, inverter. Each inverter level can generate three different voltage outputs, +Vdc, 0, and –Vdc by connecting the dc source to the ac output by different combinations of the four switches, Sa1, Sa2, Sa11, and Sa21. To obtain +Vdc, switches Sa1 and Sa21 are turned on, whereas –Vdc can be obtained by turning on switches Sa2 and Sa11. By turning on Sa1 and Sa2 or Sa11 and Sa21, the output voltage is 0. The ac outputs of each of the different fullbridge inverter levels are connected in series such that the synthesized voltage waveform is the sum of the inverter outputs. The number of output phase voltage levels m in a cascade inverter is defi ned by m = 2s+1, where s is the number of separate dc sources. An example phase voltage waveform for a 5-level cascaded H-bridge inverter with 2 SDCSs and 2 full bridges is shown in Fig. 2.
Figure 1: Single Phase Structure of a 5- Level Cascaded Multilevel Inverter
Review of Mitigation of Harmonics in Multilevel Inverters Using PSO
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Figure 2: Output Phase Voltage of 5-Level Cascaded Multilevel Inverter
SELECTIVE HARMONIC ELIMINATION Considering equal amplitude of all dc sources, the Fourier series expansion of the output voltage waveform, shown in Fig.2, will be written: (1) Where, Vn is the amplitude of nth harmonic. Switching angles are limited between zero and π/2 (0≤θi≤π/2). Because of odd quarter-wave symmetric characteristic, harmonics with even order become zero. Consequently, Vn becomes: For odd ns For even ns
(2)
The Fourier expansion for generated voltage waveform using the SHE-PWM method is given be (3) The switching angles θ1–θks must satisfy the following condition: (4) The number of harmonics which can be eliminated from the output voltage of the inverter is (s - 1). For example, to eliminate the fifth-order harmonic for a five-level inverter, equation set (5) must be satisfied. Note that the elimination of triple harmonics for the three-phase power system applications is not necessary, because these harmonics are automatically eliminated from the line-line voltage +
=( )M +
=0
In (5), modulation index M is defined as M =
(5) and
is the fundamental of the required voltage
PARTICLE SWARM OPTIMIZATION Particle Swarm Optimization (PSO) was invented by Kennedy and Eberhart1 in the mid 1990s while attempting to simulate the choreographed, graceful motion of swarms of birds as part of a sociocognitive study investigating the
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notion of “collective intelligence” in biological populations. In PSO, a set of randomly generated solutions (initial swarm) propagates in the design space towards the optimal solution over a number of iterations (moves) based on large amount of information about the design space that is assimilated and shared by all members of the swarm. PSO is inspired by the ability of flocks of birds, schools of fish, and herds of animals to adapt to their environment, find rich sources of food, and avoid predators by implementing an “information sharing” approach, hence, developing an evolutionary advantage. A complete chronicle of the development of the PSO algorithm forms merely a motion simulator to a heuristic optimization approach. Inspired initially by flocking birds, Particle Swarm Optimization (PSO) is another form of Evolutionary Computation and is stochastic in nature much like Genetic Algorithms. Instead of a constantly dying and mutating GA population we have a set number of particles that fly through the hyperspace of. the problem. A minimization (or maximization) of the problem topology is found both by a panicle remembering its own past best position and the entire group‘s (or flock’s, or swarm’s) best overall position. This algorithm has been shown to have CA like advantages without the big computational hit.The PSO algorithm is based on the concept that complex behaviour follows from a few simple rules. Each particle is determined by two vectors in Dimensional search space: the position vector Xi = [Xi1, Xi2……. XiD] and the velocity vector Vi = [Vi1, Vi2, . . . , ViDl. Each particle in the swarm refines its search through its present velocity, previous experience, and the experience of the neighbouring particles. The best position of particle i found so far is called personal best and is denoted by Pi = [Pi1, Pi2, . . . , PiD], and the best position in the entire swarm is called global best and is denoted by Pg = [Pg1, Pg2, . . . , PgD]. At first, the velocity of the ith particle on the dth dimension is updated by using (4), and then, (5) is used to modify the position of that particle Vid(t + 1) = χ [ Vid(t) + φ1r1 (Pid - Xid(t)) + φ2r2 (Pgd - Xid(t))]
(6)
Xid(t+1)=Xid(t)+Vid(t+ 1)
(7)
where φ1 and φ2 are the cogitative and social parameters, respectively. In these equations, r1 and r2 are random values uniformly distributed within [0, 1]. Vi (t) which is the velocity of ith particle at iteration‘t’ must lie in the range Vdmin < vid
(t)
< Vdmax. The parameter Vdmax determines the resolution, or fitness, with which regions are to be searched between
the present position and the target position. If Vdmax is too high, particles may fly past good solutions. If Vdmax is too small, particles may not explore sufficiently beyond local solutions. The constants C1and C2 pull each particle towards pbest and gbest positions. Low values allow particles to roam far from the target regions before being tugged back. On the other hand, high values result in abrupt movement towards, or past, target regions. Hence, the acceleration constants C1 and C2 are often set to be 2.0 according to past experiences. Suitable selection of inertia weight ‘ω’ provides a balance between global and local explorations, thus requiring less iteration on average to find a sufficiently optimal solution. As originally developed, ω often decreases linearly from about 0.9 to 0.4 during a run. In general, the inertia weight ω is set according to the following equation.
ω =ωmax −[(ωmax −ωmin ) ÷itermax ]×iter
(8)
where - ω inertia weight factor, ωmax maximum value of weighting factor, ωmin minimum value of weighting factor, itermax maximum number of iterations,iter current number of iteration Each individual moves from the current position to the next one by the modified velocity using the following equation (9)
Review of Mitigation of Harmonics in Multilevel Inverters Using PSO
P g(itd+ 1 ) = P g(itd) + V i d( t + 1 )
69
(9)
REVIEW ON APPLICATION OF PSO IN MULTILEVEL INVERTER In 2008 A.K. Al-Othman and Tamer H. Abdelhamid presents an extremely fast optimal solution of harmonic elimination of multilevel inverters with non-equal dc sources using a novel Particle Swarm Optimization (PSO) algorithm. In this paper PSO employed to compute the optimal solution set of switching angles of Multilevel Inverter. A comparison between the PSO technique and the conventional Newton-Raphson method in terms of computational times and resulted %THD is calculated; where it reveals that the PSO algorithm can be effectively used for selective harmonic elimination of multilevel inverters and results in a dramatic decrease in both the computational times and the output voltage %THD. In 2008 Chris M. Hutson, et al. investigated the application of an MDPSO algorithm for selection of a modulation sequence for a three level Five-phase motor drive. A modified discrete particle swarm (MDPSO) algorithm is used in an attempt to find the optimal space vector modulation switching sequence that results in the lowest voltage THD. Comparison of the MDPSO algorithm to an integer particle swarm optimization (IPSO) is presented for all three modulation indices (M=0.9, M=0.75, M=0.6) tested. The MDPSO algorithm performed better overall than the IPSO in terms of converging to the best solution with significantly lower iterations. In 2008 H. Taghizadeh and M. Tarafdar Hagh presents the novel particle swarm optimization technique to determine the optimum switching angles of multilevel converters to produce the required fundamental voltage while at the same time not generate lower order harmonics. This optimization method is applied to transcendental equations characterizing the harmonic content to minimize low order harmonics. Comparing the results of PSO with mathematical Methods for seven and eleven level inverter. It finds that PSO can simply find the optimum switching angles and also with comparing with Genetic Algorithm and it is clear that PSO has faster convergence with better quality solutions than GA approach to solve this problem. In 2008 R.N. Ray , et al. compute the switching angles for selected harmonic elimination (SHE) in a multilevel inverter using the particle swarm optimisation technique. The objective function derived from the SHE problem is minimised using the PSO algorithm to compute the switching angles while lower-order harmonics are eliminated. In this paper the combination of switching angles corresponding to minimum voltage THD at sufficiently close points of modulation indices with consideration of linearity between two successive points are stored in a DSP memory for online application. In 2009 Kashefi Kaviani ,et al. applies an advanced variation of Particle Swarm Optimization method to 7 to 17level inverters. Results are compared with Continuous Genetic Algorithm, as a well-known intelligent method, and one of the most successful numerical methods, namely Sequential Quadratic Programming. Results confirm that PSO completely outperforms both CGA and SQP for all cases. In 2009 Mehrdad Tarafdar Hagh, , et al. developed an algorithm based on species-based PSO (SPSO) to deal with the problem where the number of switching angles is increased and their determination using conventional iterative methods in addition to GA and simple PSO techniques is not possible. So an MSPSO algorithm with adaptive adjustment of niche radius has been proposed to determine the optimum switching angles of multilevel inverters. Simulation and experimental results are provided for an 11-level cascaded H-bridge inverter to validate the accuracy of computational results. Results show that all undesired harmonics up to 50th order have been effectively minimized at the output voltage
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waveform of inverter. Comparison of results with active harmonic elimination technique shows that the THD and the switching frequency of output voltage decreased dramatically. In 2010 Jin Wang, and Damoun Ahmadi, introduced concept of a four-simple-equation-based method. In this paper presents a different approach, which is based on equal area criteria and harmonic injection. With the proposed method, regardless of how many voltage levels are involved, only four simple equations are needed. The results of a case study with maximum of five switching angles show that the proposed method can be used to achieve excellent harmonic elimination performance for the modulation index range at least from 0.2 to 0.9. . To show the effectiveness of the proposed method in applications with large numbers of switching angles, experimental results on a 1-MVA 6000-V 17level cascade multilevel inverter are taken by the author. In 2010 H. Taghizadeh and M. Tarafdar Hagh, present the elimination of harmonics in a cascade multilevel inverter by considering the nonequality of separated dc sources by using particle swarm optimization. In addition, for a low number of switching angles, the proposed PSO approach reduces the computational burden to find the optimal solution compared with iterative methods and the resultant theory approach. The proposed method solves the asymmetry of the transcendental equation set, which has to be solved in cascade multilevel inverters. Simulation and experimental results are provided for an 11-level cascaded multilevel inverter to show the validity of the proposed method. In 2010 M. Sarvi M. R. Salimian used two algorithms: 1-genetic algorithm and 2- PSO is used to optimize THD in Multilevel inverters. Theoretical and simulated results are used to compare these techniques. Also in this paper proposes a method for optimization of specific harmonics and improving the characteristics of switching in multilevel inverters. In this method, the switching angle of each levels and the output voltage of them is determined and is used for optimization. Then the effect of changing in the output voltage of each inverter on reduction of one or more specific harmonic is analyzed. In this paper result of GA and PSO is compared and
shows that GA is better for optimizing THD in multilevel
converters. The amplitude of specific harmonics can be decreased better by changing the amplitude of each level in comparison of assuming constant amplitude. In this 2011 Rambir Singh, et al. presents a study of three optimization algorithms for different errors as variables of fitness function to find optimum gain values of a PI controller for shunt active power filters (SAPF). comparative study of PI controller tuning in a SAPF using three evolutionary algorithms (EAs), viz. bacteria foraging (BF), bacteria foraging with swarming (BFS) and particle swarm optimisation (PSO), for current harmonic mitigation. The minimization of integral time square error (ITSE) and integral time absolute error (ITAE) as performance indices is used as objective function for optimisation. The simulation results show that PSO tuned PI with ITSE as minimized parameter performs better. In 2011 Harish S Krishnamoorthy developed A novel modified-PSO based shunt active power filter was designed and simulated at different load conditions using MATLAB. An empirical equation was developed for each control parameter with respect to input and the effectiveness of the entire system was tested at different load conditions. The system evinces very good performance, by reducing the THD below 5% after the initial 4 or 5 cycles and improving PF to values as high as 0.99 for most cases based on the empirical equations; which show that the control system is a robust one for varying load conditions. This method can be used in 3-phase APFs too, applying different control schemes such as d-q control, sliding mode control, etc. The main advantages of the proposed system are that the hardware need not be changed for varying loads and there is no requirement of advanced hardware for the control system. A simple DSP can be used for controlling the entire system. For all these reasons, the authors associate good commercial value for this system in terms of its effectiveness and simplicity.
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In 2012 Rachid TALEB, et al. proposed method for the harmonic elimination strategy of a Uniform Step Asymmetrical Multilevel Inverter (USAMI) using Particle Swarm Optimization (PSO) which eliminates specified higher order harmonics while maintaining the required fundamental voltage. In this paper a seven-level USAMI is considered and the optimum switching angles are calculated to eliminate the fifth and seventh harmonics. In 2012 T.JEEVABHARATHI, V.PADMATHILAGAM proposed the method for elimination of harmonics in a Cascaded Multilevel Inverter (CMLI) by considering the non-equality of separated dc sources by using Particle Swarm Optimization (PSO) is presented. The PSO has been proposed to solve the SHE problem with nonequal dc sources in Hbridge cascaded multilevel inverters. When the resultant approach reaches the limitation of contemporary algebra software tools, the proposed method is able to find the optimum switching angles in a simple manner. The simulation and experimental results are provided for an 11-level cascaded H-bridge inverter to validate the accuracy of the computational results. In 2012 Ricardo Maldonado et al. presents the simulation and construction of a 9-level Flying Capacitor Multilevel Inverter (FCMI), with a control based on the Fundamental Frequency Switching Method (FFSM) and redundant switching states. A Particle Swarm Optimization (PSO) algorithm was developed to determine the MOSFETs firing angles to reduce the resulting Total Harmonic Distortion (THD). MATLAB/Simulink was used to simulate the FCMI and implement the PSO algorithm. A microcontroller was used to generate the sixteen different signals to control the firing angles for the hardware implementation. Simulation and experimental results confirmed the proper function of the FFSM control and capacitor balancing. To obtain a higher efficiency in the FCMI, the MOSFETs need to be replaced by Power MOSFETs with much lower Ron resistance and the capacitance need to be increased in each capacitor to achieve a FCMI with higher current rating.
CONCLUSIONS The PSO has been proposed to solve the SHE problem with equal and non equal dc source in H-bridge cascaded multilevel inverter. The proposed method is able to find the optimum switching angles in a simple manner. It also reduces both the computational burden and running time, and ensures the accuracy and quality of the calculated angles. The PSO technique proved its effectiveness in finding optimal solutions in extremely short time for different values of the dc sources, where THD was taken as a performance index to examine the effectiveness of the solution.
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